A hemispherical resonator gyroscope (HRG) is a type of gyroscope that employs a hemispherically shaped resonator (as opposed to a rotating wheel) to sense angular displacement. The HRG is a species of the group of Coriolis vibratory gyroscopes, and in particular is a “Class II” Coriolis vibratory gyroscope, members of which are geometrically symmetrical about their sensing or input axes and have degenerate, or nearly identical, resonant frequencies for the vibrations along the principal elastic axes.
An HRG generally comprises a hemispherical resonator symmetric about an input or sense axis. The resonator may be integrally formed with a supporting stem that is generally collinear with the sense axis. The resonator is typically caused to vibrate by applying an oscillating forcing signal at a frequency near the resonant frequency of the resonator. The signal may be an electrical signal and may be coupled to the resonator electrostatically. The forcing signal sets up a standing wave flex pattern, which is generally stationary when the angular rate about the input axis is zero, but which tends to rotate when the angular rate about the input axis is non-zero.
Angular displacement of the gyroscope, or its angular rate, with respect to the input axis, may be sensed by observing the flex pattern, which manifests nodes of minimum vibration amplitude, and anti-nodes of maximum vibration amplitude. HRGs may operate in open-loop and closed-loop modes. In the open-loop mode, the flex pattern is allowed to rotate, and its position or rate of rotation is sensed as a measure of the angular displacement or angular rate. In the closed-loop mode, a control system adjusts the forcing signal so as to maintain the flex pattern aligned in a chosen orientation with respect to the resonator, despite angular displacement of the gyroscope. Angular rate is measured by comparing the forcing signal required to maintain the chosen alignment of the flex pattern against a stable reference signal. Angular displacement may be obtained by integrating the rate signal. In the closed-loop mode, the control system provides a force to realign or “rebalance” the flex pattern to the chosen orientation, in the presence of an angular displacement or rate that would otherwise cause the flex pattern to shift. Accordingly, the closed-loop mode is sometimes referred to as the “force-to-rebalance” mode.
Although HRGs are generally considered to perform well, their performance is limited by several errors unless those errors are corrected. A first error relates to the tendency of the flex pattern to drift toward a drift axis defined by the geometry of the HRG apparatus. The drift tendency may be caused by imperfections in the hemispherical shape of the resonator, the presence of the electrodes, transducers, or other signal coupling devices, and other anomalies. The drift tendency is interpreted by the control system as an angular rate and therefore constitutes a bias error. A second error relates to imperfection in the effective gain of the rate-measuring signal processing system used to control the gyroscope and to furnish a rate signal from the gyroscope. Any discrepancy in the effective gain of this signal processing, including variation in sensor gain, amplifier gain, or the like, results in a scale factor error. These discrepancies or variations may occur due to device aging, temperature variation, radiation exposure, and other factors.
The scale factor error described above relates to the gyroscope control system and the associated forcing and measuring signal processing system. The resonator itself exhibits a different “geometric” scale factor which is dependent only on the geometry of the resonator—i.e., its hemispherical shape. The geometric scale factor remains nearly invariant over temperature, size, diameter, thickness, and elastic modulus of the resonator.
In some applications, scale factor and bias errors of a gyroscope system might be corrected manually by calibrating the gyroscope system during manufacturing, testing, or in a subsequent calibration step. However, in other applications, such calibration may not be feasible. For example, in space vehicle applications, the vehicle may not be reachable after launch. In other applications, the mission time may be so brief, or the factors producing the errors may vary so rapidly, that any initial calibration soon becomes stale, and manual recalibration is not feasible. Also, manual recalibration may be too expensive.
Thus, the need exists for apparatus and methods for use with gyroscope systems to allow self calibration to minimize at least scale factor and bias errors.